The engine will pull forwards regardless and the wheels can spin backwards all they like.
No ones disputing that the plane can't move forward while the conveyor is moving backwards, it can but it just means the engine needs to throttle up and it'll move forward, after all its pulling at the air in front of the prop not driving the wheels.
But this is the thing Aron, the original question stated that the conveyor speed matched the plane speed (i'm assuming they knew the knots for a given engine rpm) and set the conveyor at the same speed but backwards, in which case the plane would not pull forward until it throttled up...........just like your analogy of someone on a treadmill pulling themselves forward, yes they would overcome the motion of the treadmill but thats not 'all things being equal' is it
What the question was meant to ask i think was imagine a model plane (for now), sit it on a long dining table on top of a table cloth, pull the cloth out from under the plane and.........
WHAT WOULD HAPPEN, would it take off or wouldn't it
My take on it is NO, the wheels would spin of course but with no air flow over the wings it could never take off, now start the engine and throttle up as the cloth is pulled then yes you will move forward...........but thats
NOT what the original myth was